Unless you have case lube on your fingers, you are probably not contaminating the primers by handling. I have seen rolling cases on a case lube pad, running the case into the die to size, then with their greasy fingers pick up a primer, drop it into the priming arm, and then seating the primer. THAT can lead to contaminated primers. But if you are priming in a separate step from resizing, it's not likely.
Primers need to be "crushed" or "upset" into the primer pocket VERY slightly in order to be at the correct sensitivity. The cup needs to be bottomed out into the primer pocket "plus a thousandth or two", else they will not be as sensitive as they are designed to be. Make sure your primers are FULLY seated. There is a "feeling" you develop with your hands on the tools that gives feedback as to how they are seating. You DO NOT want primers to not be fully seated, so don't be shy about putting pressure on the tool. With that said... don't be a gorilla either.
If you have clean primer pockets, clean primers (latex gloves are NOT needed), and they are correctly seated and then struck by a firing pin with the correct velocity, and they still do not fire... you have bad primers.
To the VELOCITY of the firing pin... getting a good impression does NOT mean that you have struck the primer with adequate energy to fire it. There is an impact VELOCITY that is critical for detonation of every explosive, and a priming compound is an explosive. Strike it at a velocity less than it's detonation initiation velocity... it's not gonna go bang. You can slowly deform a primer and make a correct looking impression and it will not fire. Weak firing pin springs will do this. Impressions tell you that the firing pin is long enough. They do not tell you the SPEED at which the impression was made. It makes a difference.
Clear flash hole (no grain of tumbling media in the hole)
Correctly Seated (fully, and then a bit)
Hit with the correct firing pin impression
Hit at the correct velocity by the firing pin.